typically, a 1-d automata is thought of as spanning an infinite grid, of which you see a subsection.
therefore, the first cell in your finite representation is thought to have a neighbor of 0 (an off cell). i make a disagreement here, and think of an automaton as more ‘intelligent’; thereby knowing its boundary.
this is important to me, because representation needs to account for the fact that it is designed for a finite grid (and number of elements), and not for an infinite grid (because growth is not infinite, and, i believe, has a boundary).
therefore the ruleset grows.
no boundaries:
2 ^ 3 -> 8.
boundary on left & right:
2 ^ 2 -> 4 + 2 ^ 2 -> 4 => 8.
8 + 8 -> 16 (as opposed to 8).
a paper that studies it, but is not relevant to me at the moment:
https://arxiv.org/html/2406.06195v1